\c@sdZddlmZddlmZedddddd jd Zd Zd Zd Z dZ dZ dZ dZ dZdZdZdZdZdS(sZ Fundamental operations of dense matrices. The dense matrix is stored as a list of lists i(trange(tSymPyDeprecationWarningtfeaturet densetoolstissuei1tdeprecated_since_versions1.1cCs<|j}x,tt|D]}||||7}qW|S(sT Returns the trace of a matrix. Examples ======== >>> from sympy.matrices.densetools import trace, eye >>> from sympy import ZZ >>> a = [ ... [ZZ(3), ZZ(7), ZZ(4)], ... [ZZ(2), ZZ(4), ZZ(5)], ... [ZZ(6), ZZ(2), ZZ(3)]] >>> b = eye(4, ZZ) >>> trace(a, ZZ) 10 >>> trace(b, ZZ) 4 (tzeroRtlen(tmatlisttKtresultti((s8lib/python2.7/site-packages/sympy/matrices/densetools.pyttraces cCs#gt|D]}t|^q S(sG Returns the transpose of a matrix Examples ======== >>> from sympy.matrices.densetools import transpose >>> from sympy import ZZ >>> a = [ ... [ZZ(3), ZZ(7), ZZ(4)], ... [ZZ(2), ZZ(4), ZZ(5)], ... [ZZ(6), ZZ(2), ZZ(3)]] >>> transpose(a, ZZ) [[3, 2, 6], [7, 4, 2], [4, 5, 3]] (tziptlist(RR ta((s8lib/python2.7/site-packages/sympy/matrices/densetools.pyt transpose)scCs g|D]}t||^qS(s~ Returns the conjugate of a matrix row-wise. Examples ======== >>> from sympy.matrices.densetools import conjugate >>> from sympy import ZZ >>> a = [ ... [ZZ(3), ZZ(2), ZZ(6)], ... [ZZ(7), ZZ(4), ZZ(2)], ... [ZZ(4), ZZ(5), ZZ(3)]] >>> conjugate(a, ZZ) [[3, 2, 6], [7, 4, 2], [4, 5, 3]] See Also ======== conjugate_row (t conjugate_row(RR trow((s8lib/python2.7/site-packages/sympy/matrices/densetools.pyt conjugate=scCsXg}xK|D]C}t|dd}|dk r=|}n|}|j|q W|S(s Returns the conjugate of a row element-wise Examples ======== >>> from sympy.matrices.densetools import conjugate_row >>> from sympy import ZZ >>> a = [ZZ(3), ZZ(2), ZZ(6)] >>> conjugate_row(a, ZZ) [3, 2, 6] RN(tgetattrtNonetappend(RR R trtconjtconjrow((s8lib/python2.7/site-packages/sympy/matrices/densetools.pyRUs    cCstt|||S(sd Returns the conjugate-transpose of a matrix Examples ======== >>> from sympy import ZZ >>> from sympy.matrices.densetools import conjugate_transpose >>> a = [ ... [ZZ(3), ZZ(7), ZZ(4)], ... [ZZ(2), ZZ(4), ZZ(5)], ... [ZZ(6), ZZ(2), ZZ(3)]] >>> conjugate_transpose(a, ZZ) [[3, 2, 6], [7, 4, 2], [4, 5, 3]] (RR(RR ((s8lib/python2.7/site-packages/sympy/matrices/densetools.pytconjugate_transposenscCs*gt||D]\}}||^qS(s Augments a matrix and a column. Examples ======== >>> from sympy.matrices.densetools import augment >>> from sympy import ZZ >>> a = [ ... [ZZ(3), ZZ(7), ZZ(4)], ... [ZZ(2), ZZ(4), ZZ(5)], ... [ZZ(6), ZZ(2), ZZ(3)]] >>> b = [ ... [ZZ(4)], ... [ZZ(5)], ... [ZZ(6)]] >>> augment(a, b, ZZ) [[3, 7, 4, 4], [2, 4, 5, 5], [6, 2, 3, 6]] (R (RtcolumnR Rtelement((s8lib/python2.7/site-packages/sympy/matrices/densetools.pytaugmentscCsg}xrt|D]d}|jgxNt|D]@}||kr_||j|dq3||j|jq3WqW|S(s Returns an identity matrix of size n. Examples ======== >>> from sympy.matrices.densetools import eye >>> from sympy import ZZ >>> eye(3, ZZ) [[1, 0, 0], [0, 1, 0], [0, 0, 1]] i(RRR(tnR R R tj((s8lib/python2.7/site-packages/sympy/matrices/densetools.pyteyes   cCs||S(s Returns the ith row of a matrix Examples ======== >>> from sympy.matrices.densetools import row >>> from sympy import ZZ >>> a = [ ... [ZZ(3), ZZ(7), ZZ(4)], ... [ZZ(2), ZZ(4), ZZ(5)], ... [ZZ(6), ZZ(2), ZZ(3)]] >>> row(a, 2) [6, 2, 3] ((RR ((s8lib/python2.7/site-packages/sympy/matrices/densetools.pyRscCsCgt|D]}t|^q }g||D]}|g^q0S(sK Returns the ith column of a matrix Note: Currently very expensive Examples ======== >>> from sympy.matrices.densetools import col >>> from sympy import ZZ >>> a = [ ... [ZZ(3), ZZ(7), ZZ(4)], ... [ZZ(2), ZZ(4), ZZ(5)], ... [ZZ(6), ZZ(2), ZZ(3)]] >>> col(a, 1) [[7], [4], [2]] (R R(RR tltmatcol((s8lib/python2.7/site-packages/sympy/matrices/densetools.pytcols%cCs!||||||<||<|S(sC Returns the matrix with index1 row and index2 row swapped ((Rtindex1tindex2R ((s8lib/python2.7/site-packages/sympy/matrices/densetools.pytrowswapscCs?x8tt||D] }|||||||>> from sympy.matrices.densetools import isHermitian >>> from sympy import QQ >>> a = [ ... [QQ(2,1), QQ(-1,1), QQ(-1,1)], ... [QQ(0,1), QQ(4,1), QQ(-1,1)], ... [QQ(0,1), QQ(0,1), QQ(3,1)]] >>> isHermitian(a, QQ) False (R(RR ((s8lib/python2.7/site-packages/sympy/matrices/densetools.pyt isHermitiansN(t__doc__tsympy.core.compatibilityRtsympy.utilities.exceptionsRtwarnR RRRRRR RR#R&R)R*R+(((s8lib/python2.7/site-packages/sympy/matrices/densetools.pyts&